- Dowell, E.H. and Pezeshki, C., On necessary and sufficient conditions for chaos to occur in Duffing's equation: an heuristic approach,
J. Sound Vib. (UK), vol. 121 no. 2
pp. 195 - 200 .
(last updated on 2007/04/10)
Many different explanations have been offered for the occurrence of chaos in Duffing's equation. Holmes has derived a criterion for the onset of chaos using Melnikov theory that is based upon the initial entanglement of the unstable manifold with the stable limit cycle (1983). Moon (1985) offered a criterion based on physical principles by considering how much energy a trajectory had to possess to get out of the potential well of one of the stable limit cycles. In this paper, conclusive numerical evidence is offered that in order for steady state chaos to occur in this system, there must be a near intersection of the stable and unstable steady state limit cycles in the phase space of Duffing's equation